Editors: István Faragó, Ágnes Havasi, Zahari Zlatev

Advanced Numerical Methods for Complex Environmental Models: Needs and Availability

eBook: US $79 Special Offer (PDF + Printed Copy): US $186
Printed Copy: US $147
Library License: US $316
ISBN: 978-1-60805-777-1 (Print)
ISBN: 978-1-60805-778-8 (Online)
Year of Publication: 2013
DOI: 10.2174/97816080577881130101


High air pollution levels pose a significant threat to plants, animals and human beings. Efforts by researchers are directed towards keeping air pollution levels below well defined ‘critical‘ levels in order to maintain a sustainable atmosphere and environmental system. The application of advanced mathematical models is important for researchers to achieve this goal as efficiently as possible.

Mathematical models can be used to predict answers to many important questions about the environment. However, their application will be successful only when several theoretical and practical obstacles are efficiently removed. A successfully applicable mathematical model needs to enable researchers to

  • - Mathematically describe all important physical and chemical processes.
  • - Apply fast and sufficiently accurate numerical methods.
  • - Ensure that the model runs efficiently on modern high speed computers.
  • - Use high quality input data, both meteorological data and emission inventories, in the runs.
  • - Verify the model results by comparing them with reliable measurements taken in different parts of the spatial domain of the model.
  • - Carry out long series of sensitivity experiments to check the response of the model to changes of different key parameters.
  • - Visualize and animate the output results in order to make them easily understandable even to non-specialists.

This monograph thoroughly describes mathematical methods useful for various situations in environmental modeling - including finite difference methods, splitting methods, parallel computation, etc. - and provides a framework for resolving problems posed in relation to the points listed above. Chapters are written by well-known specialists making this book a handy reference for researchers, university teachers and students working and studying in the areas of air pollution, meteorology, applied mathematics and computer science.


High air pollution levels can cause damages to plants, animals and human beings. Therefore, it is necessary to keep them under some prescribed safe limits, which are established by different authorities. This is very challenging, but important for the modern society problem. Advanced mathematical models are one of the major tools, perhaps the most important one, which can be used to deal successfully with this important task. These models are normally described mathematically by systems of partial differential equations and have to be treated numerically on big modern computers.

One of the important problems arising when a large-scale air pollution model is used in different studies is the following: how to avoid the appearance of large numerical errors which interact with the errors caused by other reasons (such as errors due to the uncertainty of the input data or errors due to the uncertainties in the determinations of the rates of the involved chemical reactions)? The answer is in principle very simple: fine resolution discretization schemes are to be used. However, it is not very easy to treat successfully the model under consideration when fine grids are applied, because the computational tasks become very large and systems containing many millions of equations have to be solved during many time-steps. Furthermore, many studies of different phenomena related to air pollution require the use of many scenarios. Finally, very often long runs over many successive years have to be carried out. Therefore, one should:

  1. select good numerical methods,
  2. use some splitting procedure,
  3. implement them efficiently by trying to exploit the cache memories of the available computers and
  4. apply parallel computers.

The solution of these four tasks is handled in many of the chapters of the eBook and different devices for achieving efficiency are proposed.

After developing a good air pollution model it is necessary to demonstrate its usefulness by applying it in the treatment of different practical tasks. The application of air pollution models in the investigation of:

  1. distribution of the air pollution in different regions,
  2. long-range transport of air pollution of one area to another,
  3. sensitivity of air pollution levels to variation of human-made emissions,
  4. relations between air pollution levels and climate changes and
  5. prepare air pollution forecasts, is also discussed in many chapters of the eBook.

The above short description of the scope of the eBook shows very clearly that it can be useful for many different specialists interested in developing and application of large-scale air pollution models. Since the ideas are very general (systems of partial differential equations do appear in many fields of science and engineering), the eBook can also be used by specialists working in some related areas.

István Faragó, Ágnes Havasi
Department of Applied Analysis and Computational Mathematics and HAS
ELTE Research Group “Numerical Analysis and Large Networks”
Eötvös Loránd University
Pázmány P. s. 1/C, H-1117, Budapest


Zahari Zlatev

Department of Environmental Science
Aarhus University